Ok, I might be a bit too far fetched with this but here I go :-
The Full circle or sun staff represents Physical Energy and good. It is represented by the heavenly body, the Sun.
The Semi circle or moon staff represents Spiritual Energy and evil. It is represented by the heavenly body, the Moon.
The 'T' shaped staff represents Nature Energy and the unknown power and ignorance towards it. It is represented by the heavenly body, the Earth.
Basically the Sun, the Moon and the Earth are related heavenly objects. By assuming that the Earth consists of Natural Energy, the 'T' staff might represent the Earth.
Since, we all live on the Earth, we rarely acknowledge it's power i.e; Natural Energy and keep on living in ignorance. When it resurfaces, it feels like an unknown power as the Rikudou's brother basically faded from history as even Madara didn't know about him.
Thus the 'T' staff represents the Earth and Natural Energy.
What are your thoughts ?
Awesome bro never thought of that! could be legit